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Quantitative 3) Two parallel plates are separated by 1.0 mm. If the potential difference between them is 2.0 V, what is the magnitude of their surface charge densities? A) 18 nC/m2 4) A 3.0 pF capacitor consists of two parallel plates that have surface charge densities of 1.0 nC/mm2. If the potential between the plates is 27.0 kV, find the surface area of one of the plates. A) 81 mm2 5) A 100.0 pF capacitor consists of two circular plates of radius 0.40 mm. How far apart are the plates? (The value of εo is 8.85 × 10-12 C2/N•m2.) A) 0.044 μm 6) A capacitor consists of a solid sphere and a concentric hollow sphere. If the two spheres are separated by a2.0 μm gap, and the inner sphere has a radius of 7.0 mm, find the capacitance. (The value of εo is 8.85 × 10-12 C2/N•m2.) A) 2700 pF 14) Two parallel circular plates with radius 9.0 mm carrying equal-magnitude surface charge densities of 2.0 μC/m2 are separated by a distance of 2.0 mm. How much stored energy do the plates have? A) 120 nJ B) 37 nJ C) 12 nJ D) 360 nJ Answer: A Var: 36 15) Two parallel plates that are initially uncharged are separated by 1.2 mm. What charge must be transferred from one plate to the other if 11.0 kJ of energy are to be stored in the plates? The area of each plate is 19.0 mm2. A) 56 μC 18) A 1.0 μF capacitor has a potential difference of 6.0 V applied across its plates. If the potential difference across its plates is increased to 8.0 V, how much additional energy does the capacitor store? A) 14 μJ 19) A variable capacitor consists of two stacks of plates that can be adjusted so a variable amount of area of the plates faces each other. Suppose a 500.0 V potential difference is applied across a variable capacitor and it stores 5.0 mJ of energy with its plates in one position. Then it is adjusted so as to increase its capacitance, and with its plates in the new position, it stores 11.0 mJ of energy. How much does its capacitance change as its plates adjust from the first to the second position? A) 0.048 μF 20) A uniform electric field has the strength of 5.0 N/C. What is the electric energy density of the field? (The value of εo is 8.85 × 10-12 C2/N•m2.) A) 1.1 × 10-10 J/m3 25) A parallel-plate capacitor consists of two parallel, square plates that have dimensions 1.0 cm by 1.0 cm. If the plates are separated by 1.0 mm, and the space between them is filled with teflon, what is the capacitance? (The dielectric constant for teflon is 2.1.) A) 1.9 pF 26) A parallel-plate capacitor has a potential energy due to its charge of 6.00 mJ. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air is 1.0006.) A) 0.077 mJ 27) A parallel-plate capacitor has a voltage of 391 V applied across its plates, then the voltage source is removed. What is the voltage across its plates if the space between them becomes filled with mica? (The dielectric constant for mica is 5.4 and for air is 1.0006.) A) 72 V True/False 1) If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region. Answer: FALSE 2) When the electric field is zero at a point, the potential must also be zero there. Answer: FALSE 3) If the electrical potential in a region is constant, the electric field must be zero everywhere in that region . Answer: TRUE 5) If the potential is constant on a surface, then any electric field present can only be perpendicular to that surface. Answer: TRUE 9) A parallel plate capacitor is connected across a 25 V battery. If, with the battery still connected, you pull the plates apart until their separation is now twice what it originally was,the capacitance of these plates, the energy stored in the capacitor, and the excess charge on each plate are now all one half of what they originally were. Answer: TRUE Conceptual 1) Suppose a region of space has a uniform electric field, directed towards the right, as shown below. Which statement is true? A) The voltage at all three locations is the same. B) The voltage at points A and B are equal, and the voltage at point C is higher than the voltage at point A. C) The voltage at points A and B are equal, and the voltage at point C is lower than the voltage at point A. D) The voltage at point A is the highest, the voltage at point B is the second highest, and the voltage at point C is the lowest. E) None of the above Answer: C 2) If the voltage at a point in space is zero, then the electric field must be A) negative. B) zero. C) uniform. D) positive. E) impossible to determine based on the information given. Answer: E 3) The cross section of equipotential surfaces on the plane are shown below. The potential, in Volts, is indicated for three equipotential surfaces. Adjacent contours differ in potential by 10V. In which region is the magnitude of the electric field the highest? A) Region Y B) Region X C) Region Z Answer: A 4) An electric charge distribution causes the equipotential lines that are shown in the figure. Of the four labeled points, which is at the point where the electric field is stronger than the field strength at the others? A) P1 B) P2 C) P3 D) P4 Answer: B 14) In discussing energy stored by an electric field the concept of energy density is used. Why is this concept important? Answer: Electric field strength varies with position, hence the energy stored per unit volume is a meaningful concept.